This thesis presents the use of signatures within nonparametric predictive inference (NPI) for the failure time of a coherent system with a single type of components, given failure times of tested components that are exchangeable with those in the system. NPI is based on few modelling assumptions and here leads to lower and upper survival functions. We also illustrate comparison of reliability of two systems, by directly considering the random failure times of the systems. This includes explicit consideration of the difference between failure times of two systems. In this method we assume that the signature is precisely known. In addition, we show how bounds for these lower and upper survival functions can be derived based on limited information about the system structure, which can reduce computational effort substantially for specific inferential questions. It is illustrated how one can base reliability inferences on a partially known signature, assuming that bounds for the probabilities in the signature are available. As a further step in the development of NPI, we present the use of survival signatures within NPI for the failure time of a coherent system which consists of different types of components. It is assumed that, for each type of component, additional components which are exchangeable with those in the system have been tested and their failure times are available. Throughout this thesis we assume that the system is coherent, we start with a system consisting of a single type of components, then we extend for a system consisting of different types of components.